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In this paper, we investigate the interplay between the second- and the third-order nonlinearities in lithium-niobate waveguides with strong waveguide dispersion using uniform and linearly chirped poling patterns at input powers in the picojoule range. We implement the accurate unidirectional pulse propagation model to take into account all the possible nonlinear interactions inside these structures. In particular, the poling period is designed to quasi-phase-match single and multiple sum- and difference-frequency generation processes. We show how the poling period can be used as an additional degree of freedom to transform the output spectra of chip-based nonlinear waveguides in an unprecedented way.